The SLR-type camera has several features that make it more suitable for nightclub shooting.
First, its larger sensor provides a very low-noise image compared to most any point-and-shoot. That means that you can boost the ISO setting up much higher and still get a clean image with very little "graininess".
Second, you can use "fast" lenses with large apertures that are very helpful in low-light situations as well. There are some point-and-shoot cameras that have fairly wide aperture lenses, but none can match what is available for the SLR cameras.
Third, most (there are some newer ones that are quicker than in the past) point-and-shoot cameras are very slow to focus - many will take a couple of seconds or more between the time you press the shutter and the actual picture. SLR's have a fast, high-performance focusing system compared to the P&S cameras.
Flash is iffy - it is shunned in some clubs due to the distraction. But if its allowed, all SLR cameras and several high-end P&S cameras allow for a powerful externally-mounted flash.
I think that you'd do well to look into something along the lines of the Digital Rebel (300D outside the US) with its kit lens and a 50 mm f/1.8 or 1.4 lens for those club shots. The Rebel, 10D, and 20D all allow shooting modes that are almost "point-and-shoot" as far as ease of operation, but also carry the benefits of the larger format that I've listed above.